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Electronic spectra of the linear magnesium-containing carbon chains MgC2nH (n = 1–5): A CASPT2 study
Chemical Physics 360 (2009) 27–31
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Electronic spectra of the linear magnesium-containing carbon chains MgC2nH (n = 1–5): A CASPT2 study Xugeng Guo a, Junli Zhang b, Junfeng Li a, Lihui Jiang a, Jinglai Zhang a,* a b
Institute of Fine Chemistry and Engineering, College of Chemistry and Chemical Engineering, Henan University, Kaifeng 475001, China Department of Chemistry and Chemical Engineering, Huanghuai University, Zhumadian 463000, China
a r t i c l e
i n f o
Article history: Received 4 March 2009 Accepted 15 April 2009 Available online 19 April 2009 Keywords: MgC2nH (n = 1–5) CASPT2 Vertical excitation energy Linear size dependence Dissociation energy
a b s t r a c t Complete active space self-consistent-field (CASSCF) approach has been used for the geometry optimization of the X2R+ and A2P electronic states for the linear magnesium-containing carbon chains MgC2nH (n = 1–5). Multireference second-order perturbation theory (CASPT2) has been used to calculate the vertical excitation energies from the ground to selected seven excited states, as well as the potential energy curves of two 2R+ and two 2P electronic states. The studies indicate that the vertical excitation energies X2R+ transition for MgC2nH (n = 1–5) are 2.837, 2.793, 2.767, 2.714, and 2.669 eV, respecof the A2P tively, showing remarkable linear size dependence. Compared with the previous TD-DFT and RCCSD(T) results, our estimates for MgC2nH (n = 1–3) are in the best agreement with the available observed data of 2.83, 2.78, and 2.74 eV, respectively. In addition, the dissociation energies in MgC2nH (n = 1–5) are also been evaluated. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction In the past two decades, the metal monoacetylide radicals MCCH (M = Li, Na, K, Mg, Ca, Sr, and Al), have been widely investigated spectroscopically because of their potential astrophysical interest [1–25]. Indeed, the detection of the monohydrocarbon clusters C2nH (n = 1–4) in the circumstellar envelope of the carbon-rich star and in dark molecular clouds [26–28], coupled with the abundance of these metallic elements in the space, make it possible to identify these metal-bearing carbon chains in the interstellar matter. For this reason, a great many experimental and theoretical studies have been focused on these species. For example, the pure rotational spectra of LiCCH, NaCCH, and KCCH have been recorded using millimeter/submillimeter direct absorption techniques [1–4], and their ground-state properties have also been explored theoretically [5]. The ground- and excited-states properties of CaCCH and SrCCH have been determined in detail [14–24]. Recently, the electronic spectrum of AlCCH in the gas phase has been measured by means of the resonant two-color two-photon ionization (R2C2PI) technique [25]. Among the metal-containing carbon chains, the magnesium monoacetylide species MgC2H, continues to receive the extensive attention [6–13], possibly due to the fact that its isoelectronic molecule MgCN has been discovered in the circumstellar envelopes of the carbon-rich stars via radioastronomy researches [29]. Experimentally, Anderson et al. [6] presented the detection of * Corresponding author. E-mail address: [email protected] (J. Zhang). 0301-0104/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2009.04.004
MgC2H in the laboratory. Corlett et al. [7,8] and Tokaryk et al. X2R+ transition at low and high resolu[11] reported the A2P tion, respectively. For the latter, the observed excitation energy of the origin band locates at 2.83 eV. Theoretically, Woon carried out the ab initio studies on the X2R+ and A2P states, as well as X2R+ transition [10]. the A2P For the larger magnesium-capped carbon clusters, however, only a limited number of studies have been presented. To our knowledge, the gas phase electronic spectra of MgC2nH (n = 1–3) have been obtained by several experimental techniques, as well as by the RCCSD(T) calculations; the TD-DFT method has also been used for the calculations up to n = 8 [12,13]. Although in accord with the experimental findings, these theoretical studies have only been limited to the three low-lying excited states. So in this work, we report the electronic spectra of MgC2nH (n = 1–5) using the highly accurate multireference second-order perturbation theory (CASPT2) [30]. Besides improving the theoretX2R+ system, we also presical depiction of the important A2P ent the transitions from the ground to other six excited states and the potential energy curves of four out of eight electronic states. For the spectroscopists, it is our hope that the description of several excited states can provide the basis for the analysis and distribution of the spectral bands of these species.
2. Computational details The hybrid B3LYP [31–33] and CASSCF methods [34,35] along with the 6-31G* basis set have been used for the structural
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X. Guo et al. / Chemical Physics 360 (2009) 27–31
optimization of MgC2nH (n = 1–5) radicals in the X2R+ or A2P state. The nature of the B3LYP-optimized geometries has also been estimated through the frequency analyses. In the CASSCF calculations, the active spaces from the assignment of 13 electrons into 10 orbitals (4, 3, 3, 0) have been adopted for all species. CASPT2 approach using the cc-pVTZ basis set, under the B3LYPoptimized geometries, has been used to compute the vertical excitation energies from the ground to selected seven excited states. Please note that lquant-option has been used for the 2R and 2D states, while the degenerate configurations of the 2P states are not state-averaged together. In the present work, the CASSCF active space generally consists of low-energy r and p valence orbitals. For the former, the active spaces of MgC2nH (n = 1–4) are comprised of four r orbitals, namely, (4n + 3)r–(4n + 6)r, while that of MgC10H contains three r orbitals (23r–25r). For the latter, the number of p orbitals and electrons may vary with the chain size. For MgC2nH (n = 1–4), the active spaces consist of four p orbitals which correspond to 1p–4p, 2p–5p, 2p–5p, and 3p–6p, respectively. In the case of MgC10H, the active space contains five p orbitals (3p–7p). On the other hand, the potential energy curves of two 2R+ and two 2P electronic states for MgC2nH (n = 1–5) have also been obtained at the same CASPT2/cc-pVTZ level. To economize the computational cost, in the case, the p orbitals of MgC2H, MgC4H and MgC10H come from 1p–3p, 1p–4p, and 4p–7p, respectively, and the other orbitals are consistent with those used in calculations of excitation energies. In general, the oscillator strengths (f) are calculated with the expression:
f ¼
2 DEjTMj2 3
ð1Þ
where DE is the transition energy between the ground and excited states in atomic unit and TM is the transition moment in atomic unit [36]. All calculations above have been carried out by the GAUSSIAN 98 [37] and MOLPRO 2006 [38] program packages. 3. Results and discussion 3.1. Geometries for the X2R+ and A2P states CASSCF-optimized bond lengths of the X2R+ and A2P electronic states for the linear carbon chains MgC2nH (n = 1–5) are depicted in Fig. 1, together with the B3LYP optimized ground-state results for a direct comparison. It is noticeable that the good agreement is found between CASSCF and B3LYP structural parameters, with the CASSCF geometries showing the same single-triple bond alter-
nate pattern as the B3LYP ones. As shown in Fig. 1, with the increase of the chain size, the CASSCF-optimized Mg–C bond length of the X2R+ state gradually increases on going from 2.053 to 2.067 Å, while that of the A2P state gradually decreases on going from 2.039 to 2.030 Å. Moreover, the electronic promotion from X2R+ to A2P leads to the shortening of the Mg–C bonds, which is accordant with the previous theoretical studies of MgC2H and MgC4H [10,12]. Ding et al. [12] explained that the shortening of Mg–C bonds in the A2P states is mainly related to their molecular orbital nature. Frequency analyses based upon B3LYP/6-31G* vibrational calculations reveal that all the lowest bending vibrational frequencies of MgC2nH (n = 1–5) are real indicating that these species have stable structures, as noted in previous studies [12]. 3.2. Vertical excitation energy The linear carbon clusters MgC2nH (n = 1–5) have a 2R+ ground state with the electronic configuration as follows: MgC2H: 1–4r21p45–8r22p49r13p0; MgC4H: 1–6r21p47–12r22p43p413r14p0; MgC6H: 1–8r21p49–16r22–4p417r15p0; MgC8H: 1–10r21p411–19r22p420r23–5p421r16p0; MgC10H: 1–12r21p413–23r22p424r23–6p425r17p0. It is clear that for the larger chains the energy levels of 2p orbitals are lower than that of 20r for MgC8H or 24r for MgC10H, respectively. In Table 1 is summarized vertical excitation energies of selected eight electronic states with doublet spin multiplicities for MgC2nH (n = 1–5) molecules at the CASPT2/cc-pVTZ level. For comparison, the available experimental values of MgC2nH (n = 1–3) [11,12] are also presented. However, notice that the previously theoretical results of MgC2nH (n = 1–3) calculated by the RCCSD(T) and TD-DFT methods [12] are not incorporated into Table 1. For the X2R+ transition, the RCCSD(T) predicted vertical excitation A2P energies are 2.87, 2.84, and 2.81 eV, respectively, and the TDB3LYP ones are 2.92, 2.79, and 2.65 eV, respectively. As Table 1 and Fig. 2 display, the relative energy level of the excited states in MgC2nH (n = 1–5) possesses a different pattern. Among seven excited electronic states considered here, for instance, the excited states of MgC2H are in turn A2P, B2P, A2R+, A2D, A2R, B2R and B2D, while those of MgC10H are in turn A2D, A2R, B2R, B2D, A2P, A2R+, and B2P. Calculations show that the first 2P states, derived from (4n + 5)r ? (n + 2)p transition, locate at 2.837, 2.793, 2.767, 2.714, and 2.669 eV, respectively, and the corresponding oscillator strengths are the largest. For MgC2nH (n = 1–3), our estimates are in excellent agreement with the corresponding observed values [11,12], of 2.83, 2.78, and 2.74 eV, respectively. The second 2P states, arising from (n + 1)p ? (4n + 5)r excitation, lie at 4.522, 4.096, 4.111, 4.033, and 3.968 eV, respectively. In the case of the X2R+ transition, the vertical excitation energy first deA2R+ creases from MgC2H to MgC4H, then increases and again decreases from MgC6H to MgC10H, showing the same trend as the X2R+ transition. In addition, the electronic promotion from B2P (n + 1)p ? (n + 2)p, will mainly give rise to four excited states (A2D, A2R, B2R and B2D), whose corresponding vertical excitation energies decrease monotonically. 3.3. Size dependence of vertical excitation energy
Fig. 1. The bond lengths optimized by the CASSCF and B3LYP methods.
As mentioned above, Ding et al. [12] reported the vertical exciX2R+ system for MgC2nH (n = 1–8) tation energies of the A2P
X. Guo et al. / Chemical Physics 360 (2009) 27–31
29
Table 1 Vertical excitation energies (DE, eV) and oscillator strengths (f) for MgC2nH (n = 15) through CASPT2 calculations. Species
State
Transition
DE
f
MgC2H
X2 R+ A2P B2P A2R+ A2D A2R B2R B2D
. . .2p49r13p0 9r ? 3p 2p ? 9r 9r ? 10r 2p ? 3p 2p ? 3p 2p ? 3p 2p ? 3p
0.00 2.8374 (2.83)a 4.5215 4.9612 5.5710 5.6644 6.0674 6.3223
0.1873 0.0045 0.0251 0.0 0.0 0.0 0.0
X2 R+ A2P A2R+ B2P A2D A2R B2R B2D
. . .3p413r14p0 13r ? 4p 3p ? 4p 3p ? 13r 3p ? 4p 3p ? 4p 3p ? 4p 3p ? 4p
0.00 2.7925 (2.78)b 3.3473 4.0959 4.2866 4.6850 4.7677 4.9174
0.1746 0.1442 0.0043 0.00 0.00 0.00 0.00
X2 R+ A2P A2D A2R B2R B2D B2P A2R+
. . .4p417r15p0 17r ? 5p 4p ? 5p 4p ? 5p 4p ? 5p 4p ? 5p 4p ? 17r 17r ? 18r
0.00 2.7666 (2.74)b 3.2333 3.5658 3.6246 3.7677 4.1106 4.9324
0.1628 0.00 0.00 0.00 0.00 0.0077 0.0046
X2 R+ A2D A2P A2R B2R B2D A2R+ B2P
. . .5p421r16p0 5p ? 6p 21r ? 6p 5p ? 6p 5p ? 6p 5p ? 6p 4p5p ? 6p2 5p ? 21r
0.00 2.5884 2.7138 2.8735 2.9223 3.0406 3.3413 4.0328
0.00 0.1661 0.00 0.00 0.00 0.0011 0.0059
X2 R+ A2D A2R B2R B2D A2P A2R+ B2P
. . .6p425r17p0 6p ? 7p 6p ? 7p 6p ? 7p 6p ? 7p 25r ? 7p 5p6p ? 7p2 6p ? 25r
0.00 2.2352 2.5016 2.5361 2.6523 2.6686 3.2768 3.9683
0.00 0.00 0.00 0.00 0.1512 0.0013 0.0061
MgC4H
MgC6H
MgC8H
MgC10H
a b
Experimental value from Ref. [11]. Experimental value from Ref. [12].
Fig. 3. The vertical excitation energies of the A2P X2R+ transition for MgC2nH (n = 1–5) at the CASPT2, RCCSD(T) [12], and TD-B3LYP [12] levels of theory, compared with the observed values [11,12].
DE ¼ A þ Bn
ð2Þ
For the CASPT2 predicted equation A = 2.8807, B = 0.0416, and n is the number of repeating C„C units. The fitting error and correlation coefficient are 0.0073 eV and 0.9954, respectively, showing high accuracy. It is apparent that the above analytic DE n relationship could reproduce the calculated data very well. It can be seen from Fig. 3 that the CASPT2 fitting curve is almost parallel with the experimental one. As the chain size lengthens, however, the RCCSD(T), especially TD-B3LYP results, may be in poor agreement with the experiment findings. 3.4. Mg–C bond dissociation energies For further understanding the ground- and excited-states properties we have, in Figs. 4–8, respectively, described the potential energy curves of two 2R+ and two 2P electronic states in MgC2nH (n = 1–5) species with the CASPT2/cc-pVTZ level. These states, in the asymptotic limit, correlate with the four dissociation products, which are given in Table 2, as well as the corresponding dissociation energies. For MgC2nH (n = 1–5), the ground states X2R+, . . .(n + 1)p4(4n + 5)r1(n + 2)p0, correlate with the first dissociation channel, Mg (1S) + C2nH (2R+), and the corresponding dissociation energies are 74.6, 75.9, 77.4, 81.4, and 82.3 kcal mol1, respectively. It can be found that for MgC2H and MgC4H our evaluations are a little smaller than the previous RCCSD(T) results [10,12], of 76.8 and 78.3 kcal mol1, respectively. For the A2P [. . .(n + 1)p4(4n + 5)
Fig. 2. Relative energy levels of the eight electronic states in MgC2nH (n = 1–5).
using the TD-B3LYP/cc-pVTZ level, where the linear size dependence is very notable. Therefore, we carried out the linear fitting under the experiments and three levels of theory (see Fig. 3). The fitting leads to the following equation:
Fig. 4. The potential energy curves of four low-lying electronic states for MgC2H molecule.
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X. Guo et al. / Chemical Physics 360 (2009) 27–31
Fig. 5. The potential energy curves of four low-lying electronic states for MgC4H molecule.
Fig. 8. The potential energy curves of four low-lying electronic states for MgC10H molecule.
r0(n + 2)p1] and B2P [. . .(n + 1)p3(4n + 5)r2(n + 2)p0] states, the avoided crossings were discovered. If the curves crossings are not present, they will correlate with the Mg (3P) + C2nH (2R+) and Mg (3P) + C2nH (2P) asymptotes, respectively. The energies required to dissociate A2P MgC2nH to Mg (3P) + C2nH (2R+) products are 63.7, 65.3, 67.2, 74.7, and 75.4 kcal mol1, respectively. Compared with the available RCCSD(T) values [10,12], of 71.9 and 73.4 kcal mol1, respectively, our results of MgC2H and MgC4H are much smaller. The dissociation energies from B2P MgC2nH to Mg (3P) + C2nH (2P) products are 35.2, 45.1, 48.8, 51.9, and 53.6 kcal mol1, respectively. In addition, the adiabatic dissociation energies to Mg (1S) + C2nH (2P) products are 27.2, 18.1, 19.5, 23.6, and 21.3 kcal mol1, respectively. For MgC2nH (n = 2–5), the second 2 + R states exhibit another avoided crossings; however, a similar behavior is not found for MgC2H in the present work. Fig. 6. The potential energy curves of four low-lying electronic states for MgC6H molecule.
4. Conclusions
Fig. 7. The potential energy curves of four low-lying electronic states for MgC8H molecule.
Structures of linear carbon chains MgC2nH (n = 1–5) in their X2R+ and A2P electronic states have been explored by the CASSCF method with the 6-31G* basis set, in comparison with the B3LYP optimized ground-state results. The studies reveal that the agreement between CASSCF and B3LYP geometric parameters is excellent. As the chain size lengthens, furthermore, the Mg–C bond length of the X2R+ state gradually increases, while that of the A2P state gradually decreases. CASPT2 calculations show that the vertical excitation energies X2R+ transition for MgC2nH (n = 1–5) have notable of the A2P linear size dependence. Moreover, the transition energies for MgC2nH (n = 1–3) are 2.837, 2.793, and 2.767 eV, respectively, which agree very well with the available observed values of 2.83, 2.78, and 2.74 eV, respectively. On the other hand, the calculations of the dissociation energies may be helpful to the further understanding of the reactions of Mg and C2nH radicals.
Table 2 The dissociation channels and corresponding dissociation energies of the X2R+, A2P, and B2P states. State
Dissociation channel
Dissociation energies MgC2H
MgC4H
MgC6H
MgC8H
MgC10H
X2R+
Mg (1S) + C2nH (2R+)
74.6
75.9
77.4
81.4
82.3
A2P
Mg (1S) + C2nH (2P) Mg (3P) + C2nH (2R+)
27.2 63.7
18.1 65.3
19.5 67.2
23.6 74.7
21.3 75.4
B2P
Mg (3P) + C2nH (2P)
35.2
45.1
48.8
51.9
53.6
X. Guo et al. / Chemical Physics 360 (2009) 27–31
Acknowledgements This project is supported by the National Science Foundation of China (Project Nos. 20473062, 20233020, 20021002, and 20173042), the State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University (No. 200306), the Natural Science Foundation of Henan Province (Nos. 0311011200, and 200510475012) and the Ministry of Science and Technology (Nos. 2004CB719902, and 001CB1089). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
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Electronic spectra of the linear magnesium-containing carbon chains MgC2nH (n = 1–5): A CASPT2 study Xugeng Guo a, Junli Zhang b, Junfeng Li a, Lihui Jiang a, Jinglai Zhang a,* a b
Institute of Fine Chemistry and Engineering, College of Chemistry and Chemical Engineering, Henan University, Kaifeng 475001, China Department of Chemistry and Chemical Engineering, Huanghuai University, Zhumadian 463000, China
a r t i c l e
i n f o
Article history: Received 4 March 2009 Accepted 15 April 2009 Available online 19 April 2009 Keywords: MgC2nH (n = 1–5) CASPT2 Vertical excitation energy Linear size dependence Dissociation energy
a b s t r a c t Complete active space self-consistent-field (CASSCF) approach has been used for the geometry optimization of the X2R+ and A2P electronic states for the linear magnesium-containing carbon chains MgC2nH (n = 1–5). Multireference second-order perturbation theory (CASPT2) has been used to calculate the vertical excitation energies from the ground to selected seven excited states, as well as the potential energy curves of two 2R+ and two 2P electronic states. The studies indicate that the vertical excitation energies X2R+ transition for MgC2nH (n = 1–5) are 2.837, 2.793, 2.767, 2.714, and 2.669 eV, respecof the A2P tively, showing remarkable linear size dependence. Compared with the previous TD-DFT and RCCSD(T) results, our estimates for MgC2nH (n = 1–3) are in the best agreement with the available observed data of 2.83, 2.78, and 2.74 eV, respectively. In addition, the dissociation energies in MgC2nH (n = 1–5) are also been evaluated. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction In the past two decades, the metal monoacetylide radicals MCCH (M = Li, Na, K, Mg, Ca, Sr, and Al), have been widely investigated spectroscopically because of their potential astrophysical interest [1–25]. Indeed, the detection of the monohydrocarbon clusters C2nH (n = 1–4) in the circumstellar envelope of the carbon-rich star and in dark molecular clouds [26–28], coupled with the abundance of these metallic elements in the space, make it possible to identify these metal-bearing carbon chains in the interstellar matter. For this reason, a great many experimental and theoretical studies have been focused on these species. For example, the pure rotational spectra of LiCCH, NaCCH, and KCCH have been recorded using millimeter/submillimeter direct absorption techniques [1–4], and their ground-state properties have also been explored theoretically [5]. The ground- and excited-states properties of CaCCH and SrCCH have been determined in detail [14–24]. Recently, the electronic spectrum of AlCCH in the gas phase has been measured by means of the resonant two-color two-photon ionization (R2C2PI) technique [25]. Among the metal-containing carbon chains, the magnesium monoacetylide species MgC2H, continues to receive the extensive attention [6–13], possibly due to the fact that its isoelectronic molecule MgCN has been discovered in the circumstellar envelopes of the carbon-rich stars via radioastronomy researches [29]. Experimentally, Anderson et al. [6] presented the detection of * Corresponding author. E-mail address: [email protected] (J. Zhang). 0301-0104/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2009.04.004
MgC2H in the laboratory. Corlett et al. [7,8] and Tokaryk et al. X2R+ transition at low and high resolu[11] reported the A2P tion, respectively. For the latter, the observed excitation energy of the origin band locates at 2.83 eV. Theoretically, Woon carried out the ab initio studies on the X2R+ and A2P states, as well as X2R+ transition [10]. the A2P For the larger magnesium-capped carbon clusters, however, only a limited number of studies have been presented. To our knowledge, the gas phase electronic spectra of MgC2nH (n = 1–3) have been obtained by several experimental techniques, as well as by the RCCSD(T) calculations; the TD-DFT method has also been used for the calculations up to n = 8 [12,13]. Although in accord with the experimental findings, these theoretical studies have only been limited to the three low-lying excited states. So in this work, we report the electronic spectra of MgC2nH (n = 1–5) using the highly accurate multireference second-order perturbation theory (CASPT2) [30]. Besides improving the theoretX2R+ system, we also presical depiction of the important A2P ent the transitions from the ground to other six excited states and the potential energy curves of four out of eight electronic states. For the spectroscopists, it is our hope that the description of several excited states can provide the basis for the analysis and distribution of the spectral bands of these species.
2. Computational details The hybrid B3LYP [31–33] and CASSCF methods [34,35] along with the 6-31G* basis set have been used for the structural
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optimization of MgC2nH (n = 1–5) radicals in the X2R+ or A2P state. The nature of the B3LYP-optimized geometries has also been estimated through the frequency analyses. In the CASSCF calculations, the active spaces from the assignment of 13 electrons into 10 orbitals (4, 3, 3, 0) have been adopted for all species. CASPT2 approach using the cc-pVTZ basis set, under the B3LYPoptimized geometries, has been used to compute the vertical excitation energies from the ground to selected seven excited states. Please note that lquant-option has been used for the 2R and 2D states, while the degenerate configurations of the 2P states are not state-averaged together. In the present work, the CASSCF active space generally consists of low-energy r and p valence orbitals. For the former, the active spaces of MgC2nH (n = 1–4) are comprised of four r orbitals, namely, (4n + 3)r–(4n + 6)r, while that of MgC10H contains three r orbitals (23r–25r). For the latter, the number of p orbitals and electrons may vary with the chain size. For MgC2nH (n = 1–4), the active spaces consist of four p orbitals which correspond to 1p–4p, 2p–5p, 2p–5p, and 3p–6p, respectively. In the case of MgC10H, the active space contains five p orbitals (3p–7p). On the other hand, the potential energy curves of two 2R+ and two 2P electronic states for MgC2nH (n = 1–5) have also been obtained at the same CASPT2/cc-pVTZ level. To economize the computational cost, in the case, the p orbitals of MgC2H, MgC4H and MgC10H come from 1p–3p, 1p–4p, and 4p–7p, respectively, and the other orbitals are consistent with those used in calculations of excitation energies. In general, the oscillator strengths (f) are calculated with the expression:
f ¼
2 DEjTMj2 3
ð1Þ
where DE is the transition energy between the ground and excited states in atomic unit and TM is the transition moment in atomic unit [36]. All calculations above have been carried out by the GAUSSIAN 98 [37] and MOLPRO 2006 [38] program packages. 3. Results and discussion 3.1. Geometries for the X2R+ and A2P states CASSCF-optimized bond lengths of the X2R+ and A2P electronic states for the linear carbon chains MgC2nH (n = 1–5) are depicted in Fig. 1, together with the B3LYP optimized ground-state results for a direct comparison. It is noticeable that the good agreement is found between CASSCF and B3LYP structural parameters, with the CASSCF geometries showing the same single-triple bond alter-
nate pattern as the B3LYP ones. As shown in Fig. 1, with the increase of the chain size, the CASSCF-optimized Mg–C bond length of the X2R+ state gradually increases on going from 2.053 to 2.067 Å, while that of the A2P state gradually decreases on going from 2.039 to 2.030 Å. Moreover, the electronic promotion from X2R+ to A2P leads to the shortening of the Mg–C bonds, which is accordant with the previous theoretical studies of MgC2H and MgC4H [10,12]. Ding et al. [12] explained that the shortening of Mg–C bonds in the A2P states is mainly related to their molecular orbital nature. Frequency analyses based upon B3LYP/6-31G* vibrational calculations reveal that all the lowest bending vibrational frequencies of MgC2nH (n = 1–5) are real indicating that these species have stable structures, as noted in previous studies [12]. 3.2. Vertical excitation energy The linear carbon clusters MgC2nH (n = 1–5) have a 2R+ ground state with the electronic configuration as follows: MgC2H: 1–4r21p45–8r22p49r13p0; MgC4H: 1–6r21p47–12r22p43p413r14p0; MgC6H: 1–8r21p49–16r22–4p417r15p0; MgC8H: 1–10r21p411–19r22p420r23–5p421r16p0; MgC10H: 1–12r21p413–23r22p424r23–6p425r17p0. It is clear that for the larger chains the energy levels of 2p orbitals are lower than that of 20r for MgC8H or 24r for MgC10H, respectively. In Table 1 is summarized vertical excitation energies of selected eight electronic states with doublet spin multiplicities for MgC2nH (n = 1–5) molecules at the CASPT2/cc-pVTZ level. For comparison, the available experimental values of MgC2nH (n = 1–3) [11,12] are also presented. However, notice that the previously theoretical results of MgC2nH (n = 1–3) calculated by the RCCSD(T) and TD-DFT methods [12] are not incorporated into Table 1. For the X2R+ transition, the RCCSD(T) predicted vertical excitation A2P energies are 2.87, 2.84, and 2.81 eV, respectively, and the TDB3LYP ones are 2.92, 2.79, and 2.65 eV, respectively. As Table 1 and Fig. 2 display, the relative energy level of the excited states in MgC2nH (n = 1–5) possesses a different pattern. Among seven excited electronic states considered here, for instance, the excited states of MgC2H are in turn A2P, B2P, A2R+, A2D, A2R, B2R and B2D, while those of MgC10H are in turn A2D, A2R, B2R, B2D, A2P, A2R+, and B2P. Calculations show that the first 2P states, derived from (4n + 5)r ? (n + 2)p transition, locate at 2.837, 2.793, 2.767, 2.714, and 2.669 eV, respectively, and the corresponding oscillator strengths are the largest. For MgC2nH (n = 1–3), our estimates are in excellent agreement with the corresponding observed values [11,12], of 2.83, 2.78, and 2.74 eV, respectively. The second 2P states, arising from (n + 1)p ? (4n + 5)r excitation, lie at 4.522, 4.096, 4.111, 4.033, and 3.968 eV, respectively. In the case of the X2R+ transition, the vertical excitation energy first deA2R+ creases from MgC2H to MgC4H, then increases and again decreases from MgC6H to MgC10H, showing the same trend as the X2R+ transition. In addition, the electronic promotion from B2P (n + 1)p ? (n + 2)p, will mainly give rise to four excited states (A2D, A2R, B2R and B2D), whose corresponding vertical excitation energies decrease monotonically. 3.3. Size dependence of vertical excitation energy
Fig. 1. The bond lengths optimized by the CASSCF and B3LYP methods.
As mentioned above, Ding et al. [12] reported the vertical exciX2R+ system for MgC2nH (n = 1–8) tation energies of the A2P
X. Guo et al. / Chemical Physics 360 (2009) 27–31
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Table 1 Vertical excitation energies (DE, eV) and oscillator strengths (f) for MgC2nH (n = 15) through CASPT2 calculations. Species
State
Transition
DE
f
MgC2H
X2 R+ A2P B2P A2R+ A2D A2R B2R B2D
. . .2p49r13p0 9r ? 3p 2p ? 9r 9r ? 10r 2p ? 3p 2p ? 3p 2p ? 3p 2p ? 3p
0.00 2.8374 (2.83)a 4.5215 4.9612 5.5710 5.6644 6.0674 6.3223
0.1873 0.0045 0.0251 0.0 0.0 0.0 0.0
X2 R+ A2P A2R+ B2P A2D A2R B2R B2D
. . .3p413r14p0 13r ? 4p 3p ? 4p 3p ? 13r 3p ? 4p 3p ? 4p 3p ? 4p 3p ? 4p
0.00 2.7925 (2.78)b 3.3473 4.0959 4.2866 4.6850 4.7677 4.9174
0.1746 0.1442 0.0043 0.00 0.00 0.00 0.00
X2 R+ A2P A2D A2R B2R B2D B2P A2R+
. . .4p417r15p0 17r ? 5p 4p ? 5p 4p ? 5p 4p ? 5p 4p ? 5p 4p ? 17r 17r ? 18r
0.00 2.7666 (2.74)b 3.2333 3.5658 3.6246 3.7677 4.1106 4.9324
0.1628 0.00 0.00 0.00 0.00 0.0077 0.0046
X2 R+ A2D A2P A2R B2R B2D A2R+ B2P
. . .5p421r16p0 5p ? 6p 21r ? 6p 5p ? 6p 5p ? 6p 5p ? 6p 4p5p ? 6p2 5p ? 21r
0.00 2.5884 2.7138 2.8735 2.9223 3.0406 3.3413 4.0328
0.00 0.1661 0.00 0.00 0.00 0.0011 0.0059
X2 R+ A2D A2R B2R B2D A2P A2R+ B2P
. . .6p425r17p0 6p ? 7p 6p ? 7p 6p ? 7p 6p ? 7p 25r ? 7p 5p6p ? 7p2 6p ? 25r
0.00 2.2352 2.5016 2.5361 2.6523 2.6686 3.2768 3.9683
0.00 0.00 0.00 0.00 0.1512 0.0013 0.0061
MgC4H
MgC6H
MgC8H
MgC10H
a b
Experimental value from Ref. [11]. Experimental value from Ref. [12].
Fig. 3. The vertical excitation energies of the A2P X2R+ transition for MgC2nH (n = 1–5) at the CASPT2, RCCSD(T) [12], and TD-B3LYP [12] levels of theory, compared with the observed values [11,12].
DE ¼ A þ Bn
ð2Þ
For the CASPT2 predicted equation A = 2.8807, B = 0.0416, and n is the number of repeating C„C units. The fitting error and correlation coefficient are 0.0073 eV and 0.9954, respectively, showing high accuracy. It is apparent that the above analytic DE n relationship could reproduce the calculated data very well. It can be seen from Fig. 3 that the CASPT2 fitting curve is almost parallel with the experimental one. As the chain size lengthens, however, the RCCSD(T), especially TD-B3LYP results, may be in poor agreement with the experiment findings. 3.4. Mg–C bond dissociation energies For further understanding the ground- and excited-states properties we have, in Figs. 4–8, respectively, described the potential energy curves of two 2R+ and two 2P electronic states in MgC2nH (n = 1–5) species with the CASPT2/cc-pVTZ level. These states, in the asymptotic limit, correlate with the four dissociation products, which are given in Table 2, as well as the corresponding dissociation energies. For MgC2nH (n = 1–5), the ground states X2R+, . . .(n + 1)p4(4n + 5)r1(n + 2)p0, correlate with the first dissociation channel, Mg (1S) + C2nH (2R+), and the corresponding dissociation energies are 74.6, 75.9, 77.4, 81.4, and 82.3 kcal mol1, respectively. It can be found that for MgC2H and MgC4H our evaluations are a little smaller than the previous RCCSD(T) results [10,12], of 76.8 and 78.3 kcal mol1, respectively. For the A2P [. . .(n + 1)p4(4n + 5)
Fig. 2. Relative energy levels of the eight electronic states in MgC2nH (n = 1–5).
using the TD-B3LYP/cc-pVTZ level, where the linear size dependence is very notable. Therefore, we carried out the linear fitting under the experiments and three levels of theory (see Fig. 3). The fitting leads to the following equation:
Fig. 4. The potential energy curves of four low-lying electronic states for MgC2H molecule.
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X. Guo et al. / Chemical Physics 360 (2009) 27–31
Fig. 5. The potential energy curves of four low-lying electronic states for MgC4H molecule.
Fig. 8. The potential energy curves of four low-lying electronic states for MgC10H molecule.
r0(n + 2)p1] and B2P [. . .(n + 1)p3(4n + 5)r2(n + 2)p0] states, the avoided crossings were discovered. If the curves crossings are not present, they will correlate with the Mg (3P) + C2nH (2R+) and Mg (3P) + C2nH (2P) asymptotes, respectively. The energies required to dissociate A2P MgC2nH to Mg (3P) + C2nH (2R+) products are 63.7, 65.3, 67.2, 74.7, and 75.4 kcal mol1, respectively. Compared with the available RCCSD(T) values [10,12], of 71.9 and 73.4 kcal mol1, respectively, our results of MgC2H and MgC4H are much smaller. The dissociation energies from B2P MgC2nH to Mg (3P) + C2nH (2P) products are 35.2, 45.1, 48.8, 51.9, and 53.6 kcal mol1, respectively. In addition, the adiabatic dissociation energies to Mg (1S) + C2nH (2P) products are 27.2, 18.1, 19.5, 23.6, and 21.3 kcal mol1, respectively. For MgC2nH (n = 2–5), the second 2 + R states exhibit another avoided crossings; however, a similar behavior is not found for MgC2H in the present work. Fig. 6. The potential energy curves of four low-lying electronic states for MgC6H molecule.
4. Conclusions
Fig. 7. The potential energy curves of four low-lying electronic states for MgC8H molecule.
Structures of linear carbon chains MgC2nH (n = 1–5) in their X2R+ and A2P electronic states have been explored by the CASSCF method with the 6-31G* basis set, in comparison with the B3LYP optimized ground-state results. The studies reveal that the agreement between CASSCF and B3LYP geometric parameters is excellent. As the chain size lengthens, furthermore, the Mg–C bond length of the X2R+ state gradually increases, while that of the A2P state gradually decreases. CASPT2 calculations show that the vertical excitation energies X2R+ transition for MgC2nH (n = 1–5) have notable of the A2P linear size dependence. Moreover, the transition energies for MgC2nH (n = 1–3) are 2.837, 2.793, and 2.767 eV, respectively, which agree very well with the available observed values of 2.83, 2.78, and 2.74 eV, respectively. On the other hand, the calculations of the dissociation energies may be helpful to the further understanding of the reactions of Mg and C2nH radicals.
Table 2 The dissociation channels and corresponding dissociation energies of the X2R+, A2P, and B2P states. State
Dissociation channel
Dissociation energies MgC2H
MgC4H
MgC6H
MgC8H
MgC10H
X2R+
Mg (1S) + C2nH (2R+)
74.6
75.9
77.4
81.4
82.3
A2P
Mg (1S) + C2nH (2P) Mg (3P) + C2nH (2R+)
27.2 63.7
18.1 65.3
19.5 67.2
23.6 74.7
21.3 75.4
B2P
Mg (3P) + C2nH (2P)
35.2
45.1
48.8
51.9
53.6
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Acknowledgements This project is supported by the National Science Foundation of China (Project Nos. 20473062, 20233020, 20021002, and 20173042), the State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University (No. 200306), the Natural Science Foundation of Henan Province (Nos. 0311011200, and 200510475012) and the Ministry of Science and Technology (Nos. 2004CB719902, and 001CB1089). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
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